Trump met Tillerson on Tuesday and may talk to him again over the weekend, the official said. Trump appears to be in the final days of deliberations over his top diplomat with an announcement possible next week.

The transition official, who spoke on condition of anonymity, said Tillerson, 64, had moved ahead in Trump’s deliberations over 2012 Republican presidential nominee Mitt Romney, who has met Trump twice, including at a dinner in New York.

But the official said Romney was still under consideration for the job, along with John Bolton, a former U.S. ambassador to the United Nations; U.S. Senator Bob Corker of Tennessee, and retired Navy Admiral James Stavridis.

Giuliani’s withdrawal came after he was fully vetted by the Trump transition team for his overseas business ties in what was described by the Trump official as an “intense” effort by lawyers and accountants.

Giuliani, who runs a global consulting firm, was given a clean bill of health, with Trump’s aides concluding his business interests would not pose a risk to his confirmation.

Should Tillerson be nominated, his business ties, too, will come under scrutiny. Exxon Mobil has operations in more than 50 countries and boasts that it explores for oil and natural gas on six continents.

In 2011, Exxon Mobil signed a deal with Rosneft, Russia’s largest state-owned oil company, for joint oil exploration and production. Since then, the companies have formed 10 joint ventures for projects in Russia.

In 2013, Russian President Vladimir Putin awarded Tillerson his nation’s Order of Friendship.

But U.S. sanctions against Russia for its incursion into Crimea cost Exxon Mobil dearly, forcing it to scrap some projects and costing it at least $1 billion in losses. Tillerson has been a vocal critic of the sanctions.

Trump has spoken of wanting warmer relations with Moscow, which has sparked concerns in Congress that he could lift or loosen some of the sanctions on Russia.

Tillerson has been chairman and CEO of Exxon Mobil since 2006. He is expected to retire from the company next year.

Should Tillerson be nominated, climate change could be another divisive issue. The company is under investigation by the New York Attorney General’s Office for allegedly misleading investors, regulators and the public on what it knew about global warming.

What You Can Do Right Now To Stop Donald Trump's Dangerous Climate Agenda

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Strengthen city, county and state climate efforts

If the federal government refuses to stand up against climate change, it&rsquo;ll be more important than ever for cities, counties and states to pick up the slack and become climate leaders. That means committing to divest from fossil fuels, embrace clean energy, set emissions targets and <a href="http://www.c2es.org/us-states-regions/key-legislation" target="_blank">develop climate action plans</a>, among other measures.<br><br>&ldquo;The ominous signals coming out of D.C. point to even more work needed at the city and state level,&rdquo; said Kate Kiely, national media deputy director at the Natural Resources Defense Council. In November, the NRDC announced partnerships with <a href="https://www.nrdc.org/experts/christina-angelides/ten-new-cities-join-city-energy-project" target="_blank">20 cities</a> across the country from St. Paul, Minnesota, to Houston, Texas, to make strides in renewable energy.<br><br>According to Brune, cities could have&nbsp;an especially big influence&nbsp;in the climate change fight.&nbsp;&ldquo;We should be pushing cities to go 100 percent clean energy and to reject natural gas and coal and other fossil fuels,&rdquo; he said. &ldquo;A majority of people now live in cities, so this could have a dramatic impact.&rdquo; <br><br>In the U.S., at least&nbsp;<a href="http://motherboard.vice.com/read/st-petersberg-fla-100-percent-renewable-energy" target="_blank">20 cities</a> have made commitments to rely completely on clean energy. <br><br>&ldquo;People should organize and get their own cities to move forward,&rdquo; Brune said.&nbsp;<br><br>Contact your mayor, city council, or county or state representative and get them to set a timeline to stop using&nbsp;fossil fuels.